Wednesday, February 23, 2011

"You're (Not) Going to be Rich!"

Hello from Eldre'Thalas

My name is Deepcut, and I currently play on the Eldre'Thalas realm. After seeing all the fuss about "Blizzard Sanctioned Gambling" in World of Warcraft, I decided to see if I could help the community by running an experiment of my own. I emailed Markco of Just My Two Copper with my idea, and with that decided to start with my first gold-making blog.

Statistically Speaking

I am a finance major here at the local university and I also enjoy spending my time in World of Warcraft making gold. I was recently inspired to see if I could successfully perform meaningful statistical analysis on Mysterious Fortune Card. I was inspired by the blog World of Warcraft Fortunes.

The House Always Wins

What was I setting out to do (besides lose a ton of money)? At the basic level, I wanted to be able to predict the expected value when flipping a Mysterious Fortune Card with reasonable accuracy. Originally I had estimated I could calculate within 70-75 silver, however, I didn't take into account what the 5,000 gold card (I actually got one!!!) would do to the analysis. I also wanted to see if I could figure out any rhyme or reason to the possible drop rates of any individual card.

So, over the course of a couple of weeks, I gathered up over 8,000 Mysterious Fortune Cards and then tried my luck. Here's the statistics rendered from flipping the cards:

Crunching the Numbers

What does this data mean? Well, it means after flipping 8,062 cards, I am 95% confident (which is pretty good), the expected valueof a Mysterious Fortune Card is 2g28s27c +/- 1g27s53c (1g0s74c to 3g55s8c). At a cost of roughly 11g each, there is hardly a profit to be made from flipping the cards.

Also it shows that I made back a paltry 18,402g on my nearly 90,000g investment.

Here are the percentages of the flips:

A Wild Guess

If I had to speculate on the possible percentages, given the fact that I am assuming Blizzard is using nice round numbers for their probabilities, I would break it down as follows (I incorporated the data from the World of Warcraft Fortunes blog as well):

Since I know with a decent amount of confidence my expected value should be between 1g0s74c to 3g55s8c, these percentages give me an expected value of 3g6s85c, which falls well within my confidence interval while following a natural progression of lower percentages for the higher value cards.

Of course, there are 58 different Fortune Cards, and maybe the percentage is derived from a fraction of 58:

These percentages give an expected value of 2g96s21c, also within my confidence interval.

You can tweak the percentages and still easily fall within the confidence interval. So really it's anyone's guess. I would need many, many, many more flips to determine what the actual drop percentages are - roughly 32 million flips. (This is 95% confidence +/- 2 copper, with the assumption standard deviation won't change radically).

Now, these could be off by quite a bit, especially on the ones with much lower probability. I could have been very unlucky on the 1,000g card (like if they were 1/1000), or extremely lucky on the 5,000g card (like if they were 1/10000). However, I think we can all agree your chances of getting one of the rarer cards are extremely cost prohibitive, and not worth your time and effort.

Conclusion

TLDR: Don't bother flipping the cards - sell them or make Fortune Cookies, or just make glyphs from the ink. Of course, maybe you just want to see if you can get one of the 5,000g cards for bragging rights and to help peddle more cards!

Thanks for reading, and I hope you enjoyed my first foray into blogging about making gold in World of Warcraft!